We construct a ring $R$ which is a sum of two subrings $A$ and $B$ such that the Levitzki radical of $R$ does not contain any of the hyperannihilators of $A$ and $B$. This answers an open question asked by Kegel in 1964.

MSC Classifications:

16N40, 16N60 show english descriptions Nil and nilpotent radicals, sets, ideals, rings
Prime and semiprime rings [See also 16D60, 16U10] 16N40 - Nil and nilpotent radicals, sets, ideals, rings
16N60 - Prime and semiprime rings [See also 16D60, 16U10]

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